Equivalent Expressions and Simplification

An equivalent expression is an expression that has the same value as another expression for all values of the variable(s) involved.

Combine like terms: $$a + b + c + d$$ .

The perimeter is the sum of the lengths of all sides, represented as a polynomial.

Combine the coefficients of like terms: $$(5x + 3x) + (4 - 2) = 8x + 2$$ .

The distributive property states that $$a(b + c) = ab + ac$$ .

Divide the coefficients and subtract the exponents: $$\frac{6.86}{2} \times 10^{-1 - (-3)} = 3.43 \times 10^{2}$$ .

Factoring an expression means rewriting it as a product of its factors.

Multiply the coefficients and add the exponents of like bases: $$-10x^{3+1}y^{2+4} = -10x^4y^6$$ .

A polynomial is an expression consisting of variables raised to non-negative integer powers and coefficients.

Combine like terms: $$(5rt + 6rt) + (-3rw - 4rw) + (-8tw + 2tw) = 11rt - 7rw - 6tw$$ .